Egypt's new cabinet held its first meeting on Sunday and urged parties to keep their demonstrations peaceful, as a panel named to amend the constitution called on all sides to contribute, AFP reports.
In the latest violence, militants in the restive Sinai killed two soldiers and a policeman. Supporters of ousted Islamist president Mohamed Morsi, meanwhile, called for fresh rallies at foreign embassies in Cairo.
Forging ahead with an army "roadmap" for political transition, Foreign Minister Nabil Fahmy launched a public relations campaign to boost the army-backed administration's credibility abroad.
The caretaker cabinet, in a meeting chaired by prime minister Hazem Beblawi, urged "all political parties to express their opinions peacefully, and to renounce violence," after weeks of mass protests in the capital by pro- and anti-Morsi demonstrators, some of which have led to deadly clashes.
The meeting focused on Egypt's battered economy and the security situation.
Unidentified gunmen shot dead the three members of the security forces in the town of El-Arish in separate attacks, in the increasingly lawless Sinai region that has seen regular attacks on security forces since Morsi's ouster.
A newly appointed panel of four university professors and six judges also held talks on drafting a new constitution at the Shura Council, or upper house of parliament, the official MENA news agency said.
The head of the panel, the president's legal adviser Ali Awad, told reporters that the body would accept suggestions for amendments from all groups and political parties for the next week.
In the wake of the July 3 coup, Egypt's new leadership suspended the constitution that had been drawn up by an Islamist-dominated panel and adopted by referendum in December with a majority of 64 percent, but with a voter turnout of just 33 percent.
Interim president Adly Mansour appointed the constitutional committee on Saturday.
Its members have 30 days to complete their task, after which their amendments will be brought before a 50-strong body representing different groups in Egyptian society, which will submit final changes to Mansour, before he puts it to a referendum.
Work also continued on boosting the new regime's foreign relations.
Fahmy has said his ministry would "form a committee to follow what is published about the revolution abroad and to provide sound information," he told a news conference.
Morsi's overthrow has received a mixed reception abroad.
The African Union has suspended Egypt's membership, but some Gulf countries that distrusted Morsi have pledged billions of dollars in aid.
Fahmy also took a more cautious tone towards the conflict in Syria than Morsi's government did, saying Morsi's decision to cut diplomatic ties with the war-torn country would be "re-examined".
Morsi had repeatedly called on Syrian President Bashar al-Assad to resign.
"There is no intention of jihad in Syria," the former Egyptian ambassador to Washington said, in reference to calls for a holy war in Syria under Morsi's presidency.
But Fahmy also met the new leader of Syria's main opposition coalition, Ahmad Jarba, on Sunday, saying that Egypt supports the Syrian people in their aspirations.
In a boost to the new administration, King Abdullah II of Jordan on Saturday became the first foreign head of state to visit since the army ousted and detained Morsi.
King Abdullah pledged his support "for Egyptian national choices", the presidency said.
But Morsi's supporters have flatly rejected the legitimacy of the interim cabinet.
They called for fresh rallies in the capital on Sunday to demand the reinstatement of Morsi, planning marches to several foreign embassies in Cairo, including that of the United States.
But the streets around the US mission in Cairo's Garden City remained quiet, an AFP correspondent said. Soldiers and police stood guard around the embassy as usual, but no reinforcements had been called in ahead of the planned march.
At its first meeting on Sunday, the new cabinet called on "all political parties to pursue the peaceful expression of their views, and to renounce violence".
Supporters of Morsi, who was ousted after a single turbulent year of rule, have pressed demonstrations, holding marches and protests across the country since his fall.
Thousands of Morsi loyalists have been massed in Cairo's Rabaa al-Adawiya square for about three weeks, demanding his reinstatement and denouncing General Abdel Fattah al-Sisi, the army chief behind his overthrow.